Question

How do you factor `49x^6 – 100y²`?

Answer 1

`(7x^3-10y)(7x^3+10y)`

Explanation:

This expression is a `color(blue)" difference of squares"`

and In general factors as follows:

`color(red)(|bar(ul(color(white)(a/a)color(black)(a^2-b^2=(a-b)(a+b))color(white)(a/a)|)))`

now `49x^6=(7x^3)^2" and " 100y^2=(10y)^2`

`rArr49x^6-100y^2=(7x^3)^2-(10y)^2=(7x^3-10y)(7x^3+10y)`